In this paper, we use a deterministic epidemic model with memory to estimate the state of the COVID-19 epidemic in France, from early March until mid-December 2020. Our model is in the SEIR class, which means that when a susceptible individual (S) becomes infected, he/she is first exposed (E), i.e. not yet contagious. Then he/she becomes infectious (I) for a certain length of time, during which he/she may infect susceptible individuals around him/her, and finally becomes removed (R), that is, either immune or dead. The specificity of our model is that it assumes a very general probability distribution for the pair of exposed and infectious periods. The law of large numbers limit of such a model is a model with memory (the future evolution of the model depends not only upon its present state, but also upon its past). We present theoretical results linking the (unobserved) parameters of the model to various quantities which are more easily measured during the early stages of an epidemic. We then apply these results to estimate the state of the COVID-19 epidemic in France, using available information on the infection fatality ratio and on the distribution of the exposed and infectious periods. Using the hospital data published daily by Santé Publique France, we gather some information on the delay between infection and hospital admission, intensive care unit (ICU) admission and hospital deaths, and on the proportion of people who have been infected up to the end of 2020.

在本文中，我们使用具有记忆功能的确定性流行病模型来估计 2020 年 3 月初至 12 月中旬法国的 COVID-19 流行状况。我们的模型属于 SEIR 类，这意味着当易感个体（ S）被感染，他/她首先暴露（E），即尚未传染。然后他/她在一定时间内具有传染性（I），在此期间他/她可能会感染他/她周围的易感个体，最后被移除（R），即免疫或死亡。我们模型的特殊性在于，它假设暴露期和感染期的概率分布非常普遍。这种模型的大数定律极限是一个有记忆的模型（模型未来的演化不仅取决于它现在的状态，还取决于它过去的状态）。我们提出了理论结果，将模型的（未观察到的）参数与在流行病早期阶段更容易测量的各种数量联系起来。然后，我们利用有关感染死亡率以及暴露期和感染期分布的现有信息，应用这些结果来估计法国 COVID-19 的流行状况。利用法国公共卫生局每天发布的医院数据，我们收集了一些有关感染和入院之间的延迟、重症监护病房 (ICU) 入院和医院死亡以及截至 2019 年年底感染人数比例的信息。 2020.